Slack chains are more likely to derail. This only seems to happen at high cadence, which is not the best time to choose. There are 4 ways the chain can come off; 2 are usually harmless, the other 2 can be life-threatening. The harmless modes are more than a tad disconcerting IME. There is some graphic detail of the others in the FAQs.
Overtight chains will cause premature (aka rapid) bearing failure in one or both of the bottom bracket & rear hub.
I don't think that this was considered to be a big issue 40 years ago, though I was never a "club rider" so may have missed some of the lore. Be that as it may, the bushed (mostly Reynolds) chains in those days were less flexible sideways and so less likely to fall off than modern bushingless chains. Doubtless 1/8" chains are/were better than 3/32" in this respect.
We are not (yet?) very good at providing reliable quantitative guidelines as to how slack a chain can safely be, and (me too) tend towards caution. It's not a field which lends itself to controlled experimentation (aka science), for obvious reasons. But it still looks like a culture which is not yet technically mature.
OTOH my chainring is so worn that if there isn't any slack between propulsion & braking, then I worry that the chain's too tight
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